In electrolytic reduction of a nitroarene with `50%` current efficiency, `20.50`g of the electric charge. The molar mass of the compound is reduced by `2xx96500C` of electric charge. The molar mass of the compound is:

Options

A. `20.50g`
B. `10.25g`
C. `123.00g`
D. `61.50g`

Explanation

To find the molar mass of the nitroarene compound reduced in the electrolytic process, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data:**
- Weight of the compound reduced (m) = 20.50 g
- Current efficiency = 50%
- Total electric charge (Q) = \(2 \times 96500 \, C\)

2. **Calculate the Effective Charge:**
Since the current efficiency is 50%, the effective charge used in the reaction is:
\[ Q_{\text{effective}} = \text{Current Efficiency} \times Q = 0.5 \times (2 \times 96500) = 96500 \, C \]

3. **Determine the Number of Electrons Involved:**
In the reduction of nitroarene, it is stated that 6 electrons are involved in the process. This can be derived from the change in oxidation state of nitrogen from +3 to -3.

4. **Calculate the Moles of Electrons:**
Using Faraday's law, the number of moles of electrons (n) can be calculated as:
\[ n = \frac{Q_{\text{effective}}}{F} = \frac{96500}{96500} = 1 \, \text{mole of electrons} \]

5. **Relate Moles of Compound to Moles of Electrons:**
Since 6 moles of electrons are required to reduce 1 mole of the compound, we can set up the relationship:
\[ \text{Moles of compound} = \frac{n}{6} = \frac{1}{6} \, \text{moles} \]

6. **Use the Moles of Compound to Find Molar Mass:**
The molar mass (M) can be calculated using the formula:
\[ M = \frac{\text{mass}}{\text{moles}} = \frac{20.50 \, g}{\frac{1}{6}} = 20.50 \times 6 = 123 \, g/mol \]

### Final Answer:
The molar mass of the compound is **123 g/mol**.

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